Logs and Exponential

What's my Name?

100

I am the inverse operation of exponentiation

Logs

200

I am the inverse operation of logs 

Exponential

300

I am the number you raise to a power in a logarithm. In log₃(81). I am 3.

Base

400

In growth and decay functions, I am the orginal amount in an exponential function. I appear as the number in front.

Initial Value

500

I use the number e and often appear in continuous growth models.

Natural Log

Oops

100

What’s the mistake? 2³ = 6

8

200

What’s the mistake?  log₂(16)=4 

There's no mistake

300

A substance starts with 800 and decays 15% per year.
Student model:
y=800(1-0.015)^x 

The student put 0.015 instead of 0.15

400

What’s the mistake?  Solve: log⁡(x+2)=log⁡(x)+log⁡(2)

You cannot split logs across addition. Log splits apply to MULTIPLICATION not addition

500

log₂(x) + log₂ (x+30) = 6

x² + 30x = 6

x² + 30x - 6 = 0

The student forgot to do 2⁶ since the base is 2

Solve for...?

100

Solve for x.      4^x-2=4³

5

200

Solve for w.       3^4w-6=3³

2.25

300

Solve for k.        2^3k-7=16²

5

400

Solve for c.        2e^c+5=6

-3.901

500

Solve for b.         5^b=3

b=log₅(3)

Growth and Decay

100

When b > 1, what am I?

I am Growth

200

When 0 < b < 1, what am I?

Decay

300

Asymptote is ? Domain is ? Range is ?

Asymptote: y=k

Domain: All Real #'s

Range: y>k

400

f(x)=57(0.34)^x

Decaying by 66%

500

The profits of a company have been decreasing at a rate of 2.6% per year. If they had a profit of $42,000 in 2015, how much will they have in 2020?

$36,816.63

Log and Exponential

100

log(100)=?

2

200

log₂(8)=?

3

300

Rewrite in Exponential Form: log₃(81)=4

3⁴ = 81

400

Rewrite log₄(64)=3 in exponential form

4³ = 64

500

Solve for m.      2^m+4=11

log₂(11) - 4